How many different 4-digit PINs can be formed using the digits 0-9 if repetition

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Question: How many different 4-digit PINs can be formed using the digits 0-9 if repetition is allowed? (2020)

Options:

Correct Answer: 10000

Exam Year: 2020

Solution:

Each digit can be any of the 10 digits (0-9), so the total number of PINs is 10^4 = 10000.

How many different 4-digit PINs can be formed using the digits 0-9 if repetition is allowed? (2020)

How many different 4-digit PINs can be formed using the digits 0-9 if repetition is allowed? (2020)

Step 1: Understand that a 4-digit PIN consists of 4 positions, and each position can be filled with a digit from 0 to 9.
Step 2: Recognize that there are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) for each position.
Step 3: Since repetition of digits is allowed, each of the 4 positions can independently be any of the 10 digits.
Step 4: Calculate the total number of combinations by multiplying the number of choices for each position: 10 choices for the first digit, 10 for the second, 10 for the third, and 10 for the fourth.
Step 5: This can be expressed mathematically as 10 (for the first digit) * 10 (for the second digit) * 10 (for the third digit) * 10 (for the fourth digit), which is the same as 10^4.
Step 6: Calculate 10^4, which equals 10000. Therefore, there are 10000 different possible 4-digit PINs.

Combinatorics – The question tests the understanding of counting principles, specifically the multiplication principle where each digit in the PIN can be chosen independently from a set of options.
Permutations with Repetition – It assesses the ability to calculate permutations when repetition of elements (digits) is allowed.